Bayesian View of Galaxy Evolution

The Universe is pretty huge, and to understand it we need to collect vast amounts of data. The Hubble Telescope is just one of many telescopes collecting data from the Universe. Hubble alone produces 17.5 GB of raw science data each week. That means since its launch to low earth orbit in April 1990, it’s collected roughly a block of data equivalent in size to 6 million mp3 songs! With the launch of NASA’s James Webb Telescope just around the corner – (a tennis court sized space telescope!), the amount of raw data we can collect from the Universe is going to escalate dramatically. In order to decipher what this data is telling us about the Universe we need to use sophisticated statistical techniques. In this post I want to talk a bit about a particular technique I’ve been using called a Markov-Chain-Monte-Carlo (MCMC) simulation to learn about galaxy evolution.

Before we dive in into the statistics let me try and explain what I’m trying to figure out. We can model galaxy evolution by looking at a galaxy’s star formation rate (SFR) over time. Basically we want know to how fast a particular galaxy is making stars at any given time. Typically, a galaxy has an initial constant high SFR then at a time called t quench (tq) it’s SFR decreases exponentially which is characterised by a number called tau. Small tau means the galaxy stops forming stars, or is quenched, more rapidly. So overall for each galaxy we need to determine two numbers tq and tau to figure out how it evolved. Figure 1 shows what this model looks like.

Figure 1: Model of a single galaxy’s SFR over time. Showing an initial high constant SFR, follow by a exponential quench at tq.

To calculate these two numbers, tq and tau, we look at the colour of the galaxy, specifically the UVJ colour I mentioned in my last post. We then compare this to a predicted colour of a galaxy for a specific value of tq and tau. The problem is that there are many different combinations of tq and tau, how to we find the best match for a galaxy? We use a MCMC simulation to do this.

The first MC – Markov-Chain – just means an efficient random walk. We send “walkers” to have a look around for a good tq and tau, but the direction we send them to walk at each step depends on how good the tq and tau they are currently at is. The upshot of this is we quickly home in on a good value of tq and tau. The second MC – Monte Carlo – just picks out random values of tq and tau and tests how good they are by comparing the UVJ colours and our SFR model. Figure 2 shows a gif of a MCMC simulation of a single galaxy. The histograms shows the positions of the walkers searching the tq and tau space, and the blue crosshair shows the best fit value of tq and tau at every step. You can see the walkers homing in and settling down on the best value of tq and tau. I ran this simulation by running a modified version of the starpy code.

Figure 2: MCMC simulation for a single galaxy, pictured in the top right corner. Main plot shows density of walkers. Marginal histograms show 1D projections of walker densities. Blue crosshair shows best fit values of tq and tau at each step.

The maths that underpins this simulation is called Bayesian Statistics, and it’s quite a novel way of thinking about parameters and data. The main difference is that instead of treating unknown parameters as fixed quantities with associated error, they are treated as random variables described by probability distributions. It’s quite a powerful way of looking at the Universe! I’ve left all of the gory maths detail about MCMC out but if you’re interested an article by a DPhil student here at Oxford does are really good job of explaining it here.

So how does this all relate to galaxy morphology, and Galaxy Zoo classifications? I’m currently running the MCMC simulation showing in Figure 2 over the all the galaxies in the COSMOS survey. This is really cool because apart from getting to play with the University of Oxford’s super computer (544 cores!), I can use galaxy zoo morphology to see if the SFR of a galaxy over time is dependent on the galaxy’s shape, and overall learn what the vast amount of data I have says about galaxy evolution.